#### Answer

The required current is $2.8~A$

#### Work Step by Step

We can write an expression for the initial stored energy:
$U_1 = \frac{1}{2}LI_1^2$
We can find the current when the stored energy is double:
$U_2 = 2\times U_1$
$\frac{1}{2}LI_2^2 = 2\times \frac{1}{2}LI_1^2$
$I_2^2 = 2 I_1^2$
$I_2 = \sqrt{2}~ I_1$
$I_2 = (\sqrt{2})~ (2.0~A)$
$I_2 = 2.8~A$
The required current is $2.8~A$